Near-Optimal Sparse Sensing for Gaussian Detection with Correlated Observations

TL;DR

This paper introduces practical greedy algorithms for near-optimal sparse sensor selection in Gaussian detection problems with correlated observations, offering computational efficiency over traditional convex relaxation methods.

Contribution

It leverages submodularity to develop low-complexity greedy algorithms for large-scale sensor subset selection in correlated Gaussian detection tasks.

Findings

Algorithms achieve near-optimal detection performance.

Reduced computational complexity compared to convex methods.

Applicable to large-scale spatial sensing problems.

Abstract

Detection of a signal under noise is a classical signal processing problem. When monitoring spatial phenomena under a fixed budget, i.e., either physical, economical or computational constraints, the selection of a subset of available sensors, referred to as sparse sensing, that meets both the budget and performance requirements is highly desirable. Unfortunately, the subset selection problem for detection under dependent observations is combinatorial in nature and suboptimal subset selection algorithms must be employed. In this work, different from the widely used convex relaxation of the problem, we leverage submodularity, the diminishing returns property, to provide practical near optimal algorithms suitable for large-scale subset selection. This is achieved by means of low-complexity greedy algorithms, which incur a reduced computational complexity compared to their convex counterparts.